As in the scalar case, the existence of the sequence of matrix-valued orthogonal polynomials can be equivalently restated as the existence of the solution to a certain (matrix-valued) Riemann–Hilbert boundary value problem, as it has been proven in [1]}. This is a general result that does not depend on the particular form of the measure \({W}(s;x)\)  and we make reference to [1]} for its general formulation. Applied to our case, we have the following proposition:
